Prove, using properties of determinants: `|y+k y y y y+k y y y y+k|=k^2(3y+k)`

Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[ y, y, y+k]|=k^2(3y+k)

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

k x + 3y = k - 3, 12 x + ky = k

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

kx + 3y = 3, 12 x + k y = 6 .

For what value of k system of equations 3x + 4y = 19, y - x = 3 and 2x + 3y = k has a solution ?

3x - y - 5 = 0 , 6x - 2y + k = 0 ( k ne 0 )

Find the value of x, if 2x + 3y + k = 12 and x + 6y + 2k = 18

If k_r is the coefficient of y^(r - 1) in the expansion of (1 + 2y)^10 , in ascending powers of y , determine 'r' when (k_(r + 2))/(k_r) = 4

{:(2x - 3y = k),(4x + 5y = 3):}